The spin of an electron confined into a lateral semiconductor quantum
dot has been proposed as a possible physical realization of a
qubit. While the spin has the advantage of large decoherence times,
operations with more than one qubit will necessarily involve orbital
degrees of freedom, namely, charge, which is much more prone to
decoherence. There are also alternative quantum dot qubit proposals
that are entirely based on charge. We have used a realistic model to
quantify the limitations imposed by acoustic phonons on the operation
of quantum dot-based qubits. Our treatment includes essential aspects
of the setup geometry, wave function profile and materials
characteristics. The time dependence of the qubit density matrix is
the presence of a phonon bath solved within the Born-Markov
approximation. We find that the inclusion of geometric form factors
makes the phonon-induced decoherence rates in double dot charge qubits
nearly one order of magnitude lower than estimates previously in the
literature. Moreover, our theoretical prediction for the quality
factor of coherent charge oscillations based on phonon decoherence are
higher than the values recently observed experimentally. This allows
us to conclude that phonons are not the primary source of decoherence
in double quantum dot qubits.

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